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Prove the Following Trigonometric Identities `Cos^2 a + 1/(1 + Cos^2 A) = 1` - Mathematics

Prove the following trigonometric identities

`cos^2 A + 1/(1 + cos^2 A) = 1`

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Solution

We know that

`sin^2 A + cos^2 A = 1`

`cosec^2 A - cot^2 A = 1`

So,

`cos^2 A + 1/(1 + cot^2 A) = cos^2 A + 1/(cosec A)`

`= cos^2 A + (1/cosecA)^2`

`= cos^2 A + (sin A)^2`

`= cos^2 A + sin^2 A`

= 1

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 11 Trigonometric Identities
Exercise 11.1 | Q 9 | Page 43
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